There are `n ` ways to choose the child that will not get any toy.<br>
There are `C(n,2)` ways to choose `2` toys for a child that will have two toys. <br>
There are `n-1` ways to choose the child, who will get the `2` toys.<br>
There are `(n-2)!` ways to distribute the rest `n-2` toys to the rest `n-2` children.<br>
`:.` Total number of ways ` = n*C(n,2)*(n-1)*(n-2)! = n!C(n,2)`.